On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing

R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer International Publishing, Cham, 2016, pp. 256–267.

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Conference Paper | Published | English
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Abstract
Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane.
Publishing Year
Date Published
2016-04-09
Proceedings Title
Discrete Geometry for Computer Imagery
Volume
9647
Page
256-267
Conference
DGCI: International Conference on Discrete Geometry for Computer Imagery
Conference Location
Nantes, France
Conference Date
2016-04-18 – 2016-04-20
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Biswas R, Bhowmick P. On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing. In: Discrete Geometry for Computer Imagery. Vol 9647. Lecture Notes in Computer Science. Cham: Springer International Publishing; 2016:256-267. doi:10.1007/978-3-319-32360-2_20
Biswas, R., & Bhowmick, P. (2016). On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing. In Discrete Geometry for Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-32360-2_20
Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry for Computer Imagery, 9647:256–67. Lecture Notes in Computer Science. Cham: Springer International Publishing, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.
R. Biswas and P. Bhowmick, “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing,” in Discrete Geometry for Computer Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267.
Biswas R, Bhowmick P. 2016. On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing. Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer ImageryLecture Notes in Computer Science vol. 9647. 256–267.
Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for Computer Imagery, vol. 9647, Springer International Publishing, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.

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